You can see if you're on the right track with exercises because the text has solutions and hints in the back.
This undergrad text is extremely clear, with lots of examples and exercises. The text is carefully written and the clear and precise style makes it an easy read. The book contains many instructive examples and a wealth of exercises including solutions.
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Steinbauer, Monatshefte fur Mathematik, Vol. Plenty of cross-references are included to point the reader to relevant material covered earlier in the book. It is extensively cross-referenced, has a good index, a separate index of symbols Very Good Feature , and complete solutions to all the exercises.
Linear Functional Analysis
It has numerous examples, and is especially good in giving both examples of objects that have a given property and objects that do not have the property. Further highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book.
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Inner Product Spaces Hilbert Spaces. Compact Operators. Integral and Differential Equations.
Linear Functional Analysis : Bryan P. Rynne :
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